On Approximation of Gaussian Q-Function and its Applications

Abstract

In this paper, a novel closed-form expression for $Q$ -function integral-related approximation problems is proposed. The expression model is based on the Maclaurin-Taylor series expansion and can be used not only for studying average symbol error probability (ASEP) performance of the wireless communication systems in the Nakagami fading channels but also for applications which involve $Q$ -function approximation. The contribution of this paper lays mainly in three parts: (1) we derive a closed-form $Q$ -function approximation expression for the narrow-band Nakagami fading channel in order to study ASEP performance of deferentially encoded QPSK (DE-QPSK) modulation schemes; (2) we derive a closed-form metric to evaluate the average bit error rate (ABER) performance of the BPSK in the existence of the residual timing offset; (3) we derive a novel closed-form expression for the ABER performance for the ultra-wide-hand (UWB) fading channels.